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### Divide by a Fraction

```
Date: 03/19/97 at 18:05:06
From: James Farrell
Subject: Divide by a Fraction

Dear Dr. Math,

How do you divide a whole number by a fraction?  Consider:

5
--------
1
---
2

If you express it as:

5
---
1                 5         2
--------      =     ---   x   ---    =    10
1                 1         1
---
2

Why did I end up with 10?  I'm sure the answer should be 2.5.  Where
did I go wrong?

Thanks,
Tim Farrell
```

```
Date: 03/21/97 at 04:19:54
From: Doctor Mitteldorf
Subject: Re:  Divide by a Fraction

Dear Tim,

Lots of people find this confusing.  If you divide 5 by 2, the
answer is 2.5.  If you divide 5 by 1/2, do you expect the same thing
as dividing by 2?

If you divide by a number bigger than 1, it always reduces the
number. If you divide by 1, it doesn't change anything.  Does that
make you think that dividing by a fraction less than 1 should INCREASE
the number?

How many kids can you serve with 5 cookies if each kid gets 2 cookies?
You can serve 2 kids (with enough left over for 1/2 a kid).

How many kids can you serve with 5 cookies if each kid gets 1/2 a
cookie?  That's 5 divided by 1/2.

-Doctor Mitteldorf,  The Math Forum
Check out our web site!
```
Associated Topics:
Elementary Fractions

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